Distributed knowledge: Difference between revisions

Revision as of 07:14, 27 January 2020

Revision as of 06:37, 15 March 2020

Line 7:

== Example ==

The logicians Aaleyah and Isko are sitting in their dark office wondering whether or not it is raining outside. Now, none of them actually knows, but Aaleyah knows something about her friend Yu Yan, namely that Yu Yan wears her red coat [[only if]] it is raining. IskoBob does not know this, but he just saw Yu Yan, and noticed that she was wearing her red coat. Even though none of them knows whether or not it is raining, it is ''distributed knowledge'' amongst them that it is raining. If either one of them tells the other what they know, it will be clear to the other that it is raining.

If we denote by <math>\varphi</math> that Yu Yan wears a red coat and with <math>\varphi \Rightarrow \psi</math> that if Yu Yan wears a red coat, it is raining, we have

Line 13:

: <math>(K_b\varphi \land K_a(\varphi \Rightarrow \psi)) \Rightarrow D_{a,b}\psi</math>

Directly translated: IskoBob knows that Yu YanCarol wears a red coat and Aaleyah knows that if Yu YanCarol wears a red coat it is raining. Together,so together they know that it is raining.

Distributed knowledge is related to the concept [[Wisdom of the crowd]]. Distributed knowledge reflects the fact that "no one of us is smarter than all of us."